Calculation of residence time distributions of intravascular radioactive tracers in fields of external registration


Because of the physiological significance of the mean velocity of blood flow, indicator dispersion models are of special interest and posses practical relevance, if biological and extraneous variables can be altered. The variables being considered are flow characteristics of the streaming blood, tracer distribution at the entrance into the flow system, and the area in which impulses are collected to form the time-activity curve. Using a simplified version of the general convective diffusion equation (diffusion model) in which the diffusion constant D includes all propagation and mixing of the tracer, a simple numerical method can be applied. The method is used to determine influences of injection and changed regions of interest on the time-activity curve and the following parameters: appearance times, peak times, mean circulation times, and the times of the first inflection points. For this purpose, the range of D was determined in 14 patients by applying experimental data to the model. The calculations on the variables show, that the advantage of this method is its applicability to any experimental case by simply adapting the input data to the recordings.

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cross-sectional area of the flow tube

c, c0 :



v·Z/D (Bodenstein-number)

D :

mixing coefficient of the diffusion model


dimensionless initial indicator concentration

F :


L :

width of the detector field on the x-axis

t :


T :


U, u :

c/c 0 (solution of the partial differential equation; of the difference equation)

v :

mean flow velocity

V :

volume of the flow system

x :

space coordinate in flow direction

Z :

length of the flow system






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Knapp, W.H., Lüdecke, H.J. & Doll, J. Calculation of residence time distributions of intravascular radioactive tracers in fields of external registration. Eur J Nucl Med 4, 471–477 (1979).

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  • Diffusion Equation
  • Dispersion Model
  • Diffusion Constant
  • Circulation Time
  • Practical Relevance